Motor disability is a dominant and restricting symptom in multiple sclerosis, yet its neuroimaging correlates are not fully understood. We apply statistical and machine learning techniques on multimodal neuroimaging data to discriminate between multiple sclerosis patients and healthy controls and to predict motor disability scores in the patients. We examine the data of sixty-four multiple sclerosis patients and sixty-five controls, who underwent the MRI examination and the evaluation of motor disability scales. The modalities used comprised regional fractional anisotropy, regional grey matter volumes, and functional connectivity. For analysis, we employ two approaches: high-dimensional support vector machines run on features selected by Fisher Score (aiming for maximal classification accuracy), and low-dimensional logistic regression on the principal components of data (aiming for increased interpretability). We apply analogous regression methods to predict symptom severity. While fractional anisotropy provides the classification accuracy of 96.1% and 89.9% with both approaches respectively, including other modalities did not bring further improvement. Concerning the prediction of motor impairment, the low-dimensional approach performed more reliably. The first grey matter volume component was significantly correlated (R = 0.28-0.46, p < 0.05) with most clinical scales. In summary, we identified the relationship between both white and grey matter changes and motor impairment in multiple sclerosis. Furthermore, we were able to achieve the highest classification accuracy based on quantitative MRI measures of tissue integrity between patients and controls yet reported, while also providing a low-dimensional classification approach with comparable results, paving the way to interpretable machine learning models of brain changes in multiple sclerosis.